Help with Trigonometric Integral  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Help with Trigonometric Integral

Postby paulh428 on Wed Apr 27, 2011 11:23 pm

Hey everyone. This is my first post. I just need help with this problem in Calculus II. The problem states: Integrate the trigonometric integral: Integral of sin ^ 2 (5x) * cos (2x) dx. I wasn't sure how to approach it. Thanks for any help. BTW, this is what I have so far:

I've moved it around a little using trig identities:

Integral of (1 - cos ^ 2 (5x)) cos (2x) dx

= Integral of (cos (2x) - cos ^ 2 (5x) * cos (2x)) dx

= [1/2 * sin (2x)] - Integral of (cos ^ 2 (5x) * cos (2x)) dx
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Re: Help with Trigonometric Integral  TOPIC_SOLVED

Postby Martingale on Thu Apr 28, 2011 1:24 am

paulh428 wrote:Hey everyone. This is my first post. I just need help with this problem in Calculus II. The problem states: Integrate the trigonometric integral: Integral of sin ^ 2 (5x) * cos (2x) dx. I wasn't sure how to approach it. Thanks for any help. BTW, this is what I have so far:

I've moved it around a little using trig identities:

Integral of (1 - cos ^ 2 (5x)) cos (2x) dx

= Integral of (cos (2x) - cos ^ 2 (5x) * cos (2x)) dx

= [1/2 * sin (2x)] - Integral of (cos ^ 2 (5x) * cos (2x)) dx



use the following





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Re: Help with Trigonometric Integral

Postby paulh428 on Thu Apr 28, 2011 2:39 am

Thank you. I actually used it that way after this post. Not sure if what I have now is the correct answer but it was a long one nonetheless. Thank you very much. :D
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Re: Help with Trigonometric Integral

Postby Martingale on Thu Apr 28, 2011 2:50 am

Martingale wrote:






paulh428 wrote:Thank you. I actually used it that way after this post. Not sure if what I have now is the correct answer but it was a long one nonetheless. Thank you very much. :D















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